Consider the parameter regime where the deterministic system has three fixed points: one stable, one saddle, and one unstable. (Parameter values are listed in Appendix \ref{sec:type-i}.) A phase plane diagram of the deterministic dynamics is shown in Fig. \ref{fig:type1a_pp1}(a). The stable manifold of the saddle defines a threshold for excitation. A deterministic trajectory starting to the left of the threshold quickly converges to the stable fixed point. On the other hand, when starting to the right of the threshold, the trajectory exhibits a transient increase in voltage as it travels around the unstable fixed point before reaching the stable fixed point. Hence, a noise induced action potential can be broken into two phases: a slower initiation phase and a faster transient spike in voltage followed by a return to the stable fixed point. The initiation phase is a fluctuation-induced spontaneous transition from the stable fixed point to the threshold. Once the threshold is reached, the return to the stable fixed point is dominated by the deterministic forces rather than ion channel fluctuations. The most likely path taken during the return phase is along one of the two branches of the unstable manifold (see the green curve Fig. \ref{fig:type1a_pp1}(a)). The right branch leads to an excitable event and the left branch leads directly back to the stable fixed point. Fig. \ref{fig:type1a_pp1}(b) shows a representative stochastic trajectory obtained by simulation (see Appendix \ref{sec:monte-carlo-simul}).